A method of near-field trapping high and low refractive index Rayleigh particles was proposed using a binary phase Subwavelength Fresnel Zone Plate (SFZP) illuminated by the double-ring-shaped vortex beam. Based on the angular spectrum representation, the distribution of SFZP′s diffraction field was calculated. Bright and dark spots can be generated in the near field of the SFZP by changing the truncation parameter (β) and the vortex angle (δ) of the incident beam. Numerical results show that the SFZP can generate a subwavelength three-dimensional (3D) bright spot in the near-field region when β=1.09 and δ=0. The tiny bright spot can be used to stably trap a gold particle with radius 19 nm, whose refractive index is higher than that of the ambient medium. The axial and transverse trap distances are respective 0.4921λ and 0.2844λ. When β=1.45 and δ=0.414π, a 3D dark spot surrounded by a light shell can be formed in the near-field region. An air bubble with radius 30 nm is stably trapped at the center of this subwavelength dark spot. The refractive index of the air bubble is lower than the ambient medium. The axial and transverse trap distances are 0.62λ and 0.3081λ. The trap distance obtained under two conditions is less than that in the conventional far-field trap system. The single trap system can be used to accurately trap two types of Rayleigh particles with different refractive indices.